(40+2x)(20+2x)=2400

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Solution for (40+2x)(20+2x)=2400 equation: 


Simplifying
(40 + 2x)(20 + 2x) = 2400

Multiply (40 + 2x) * (20 + 2x)
(40(20 + 2x) + 2x * (20 + 2x)) = 2400
((20 * 40 + 2x * 40) + 2x * (20 + 2x)) = 2400
((800 + 80x) + 2x * (20 + 2x)) = 2400
(800 + 80x + (20 * 2x + 2x * 2x)) = 2400
(800 + 80x + (40x + 4x2)) = 2400

Combine like terms: 80x + 40x = 120x
(800 + 120x + 4x2) = 2400

Solving
800 + 120x + 4x2 = 2400

Solving for variable 'x'.

Reorder the terms:
800 + -2400 + 120x + 4x2 = 2400 + -2400

Combine like terms: 800 + -2400 = -1600
-1600 + 120x + 4x2 = 2400 + -2400

Combine like terms: 2400 + -2400 = 0
-1600 + 120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-400 + 30x + x2) = 0

Factor a trinomial.
4((-40 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve:

Simplifying
-40 + -1x = 0

Solving
-40 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '40' to each side of the equation.
-40 + 40 + -1x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1x = 0 + 40
-1x = 0 + 40

Combine like terms: 0 + 40 = 40
-1x = 40

Divide each side by '-1'.
x = -40

Simplifying
x = -40

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-40, 10}

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